Universal flows of closed subgroups of $S_{\infty}$ and relative extreme amenability

Lionel Nguyen van Thé (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

This paper is devoted to the study of universality for a particular continuous action naturally attached to certain pairs of closed subgroups of $S_{\infty}$. It shows that three new concepts, respectively called relative extreme amenability, relative Ramsey property for embeddings, and relative Ramsey property for structures, are relevant in order to understand this property correctly. It also allows to provide a partial answer to a question posed by Kechris, Pestov and Todorcevic.

Mots clés: universal flow; Extreme amenability; relative extreme amenability; relative Ramsey property; Fraïssé theory; Ramsey theory; universal flow.

Domaines: Logique [math.LO]; Combinatoire [math.CO]; Systèmes dynamiques [math.DS]; Théorie des groupes [math.GR]

Lionel Nguyen van Thé. Universal flows of closed subgroups of $S_{\infty}$ and relative extreme amenability. Fields Institute Communications, 2013, 68, pp.229-245. ⟨hal-00662494⟩